Question: $\dfrac{ -5l - 8m }{ -9 } = \dfrac{ -3l - 3n }{ -5 }$ Solve for $l$.
Explanation: Multiply both sides by the left denominator. $\dfrac{ -5l - 8m }{ -{9} } = \dfrac{ -3l - 3n }{ -5 }$ $-{9} \cdot \dfrac{ -5l - 8m }{ -{9} } = -{9} \cdot \dfrac{ -3l - 3n }{ -5 }$ $-5l - 8m = -{9} \cdot \dfrac { -3l - 3n }{ -5 }$ Multiply both sides by the right denominator. $-5l - 8m = -9 \cdot \dfrac{ -3l - 3n }{ -{5} }$ $-{5} \cdot \left( -5l - 8m \right) = -{5} \cdot -9 \cdot \dfrac{ -3l - 3n }{ -{5} }$ $-{5} \cdot \left( -5l - 8m \right) = -9 \cdot \left( -3l - 3n \right)$ Distribute both sides $-{5} \cdot \left( -5l - 8m \right) = -{9} \cdot \left( -3l - 3n \right)$ ${25}l + {40}m = {27}l + {27}n$ Combine $l$ terms on the left. ${25l} + 40m = {27l} + 27n$ $-{2l} + 40m = 27n$ Move the $m$ term to the right. $-2l + {40m} = 27n$ $-2l = 27n - {40m}$ Isolate $l$ by dividing both sides by its coefficient. $-{2}l = 27n - 40m$ $l = \dfrac{ 27n - 40m }{ -{2} }$ Swap signs so the denominator isn't negative. $l = \dfrac{ -{27}n + {40}m }{ {2} }$